Solving Multistep Inequalities

Front

What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving addition, subtraction, multiplication, or division.

Front

How do you solve the inequality -3 ≤ 2x - 1 ≤ 5?

Back

Add 1 to all parts: -2 ≤ 2x ≤ 6. Then divide by 2: -1 ≤ x ≤ 3.

Front

What does the solution -1 ≤ x ≤ 3 represent on a number line?

Back

It represents all numbers between -1 and 3, including -1 and 3.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true simultaneously, while 'or' means at least one condition must be true.

Front

How do you graph the inequality x > 2?

Back

Draw a number line, place an open circle at 2, and shade to the right.

Front

What does the solution x ≤ -3 look like on a number line?

Back

Draw a number line, place a closed circle at -3, and shade to the left.

Front

What is the solution to the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides: x ≤ 8.

Front

What does the notation (−∞, 8] mean?

Back

It represents all numbers less than or equal to 8.

Front

How do you solve the inequality 3x - 4 > 5?

Back

Add 4 to both sides: 3x > 9. Then divide by 3: x > 3.

Front

What is the solution to the inequality 2x + 3 < 11?

Back

Subtract 3 from both sides: 2x < 8. Then divide by 2: x < 4.